This invention claims the priority of Japanese Patent Application No. 26353/1994 filed on Jan. 27, 1994, which is incorporated herein by reference. 1 EPO 551 730 A1 proposes a method of producing a flat CVD diamond film. A diamond film can be synthesized on a suitable non-diamond substrate by the chemical vapor deposition (CVD) method. However, the diamond film suffers a tensile stress which is caused by growth defects or "intrinsic strain". The intrinsic strain increases in proportion to the thickness of the diamond film. When a diamond film has been deposited on a non-diamond substrate and the substrate is eliminated by some solvent, the diamond film bends or breaks due to the release of the stress. The prior art suggestes a method of making a flat self-supporting diamond film while preventing deformation. The method includes the steps of preparing a convex substrate having a predertermined curvature for offsetting any bending due to the expected tensile stress, synthesizing a diamond film by a CVD method on the convex substrate and removing the convex substrate. The resulting diamond film is a free-standing film (or self-supporting film). Since the diamond film is grown on the convex substrate, the diamond film shares the convex shape of the substrate. When the film is separated from the substrate, the stress is released in the self-supporting film. The inner stress causes the top surface to shrink and the bottom surface to elongate. Since the diamond film had originally been convex, the film deforms in the direction for decreasing the bend. The release of the inner stress transforms the originally-convex film into a flat one, if the deformation caused by the inner stress exactly equals the original convex bend. Then the prior art fixes the flat, self-supporting film on a polishing plate, polishes the film in a polishing machine and provides a flat, smooth self-supporting film.